Raman and electronic absorption spectra corresponding to the S0-S2 electronic transition of various carotenoid and polyene molecules are theoretically analyzed using the density functional theory (DFT) approach. The results demonstrate the linear dependence between the frequency of the so-called ν1 band corresponding to the C═C stretching modes in the Raman spectra and the S0-S2 electronic transition for molecules of different conjugation lengths. From these calculations the following relationship have been identified: (i) the effective conjugation length shortens in conformers of carotenoids containing β-rings whereas it increases in polyene upon s-cis isomerization at their ends, (ii) methyl groups connected to the conjugated chain of carotenoids induce a splitting of the ν1 band in the Raman spectra, (iii) the effective conjugation lengths of all-trans-polyenes and corresponding all-trans-carotenoids are the same as follows from the Raman ν1 frequency, but they are different as defined from S0-S2 electronic transition energies. The results well correlate with the experimental observations.

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